In order to suppress reduction in the performance and service life of a battery that is attributable to repeated charging and discharging with no full charging in a vehicle such as a battery-mounted car, refresh charging is performed in a case where, for example, the elapsed time from full charging becomes equal to or longer than predetermined time. The refresh charging is, for example, realized by allowing an engine operation to continue with the upper limit voltage during the charging being set to be higher than usual. When the refresh charging is executed in a vehicle in which idle reduction control (also called start and stop control) for stopping the engine in a case where the vehicle speed becomes equal to or less than a predetermined value can be executed, the engine cannot be stopped even in a case where an engine stop condition is satisfied, and thus fuel economy may be reduced. A method for performing the pre-charging prior to the execution of the refresh charging to increase the state of charge (SOC) of the battery and shortening the refresh charging period has been suggested (Patent Literature 1). The execution of the idle reduction control is allowed during this pre-charging.